Parity-induced Selmer Growth For Symplectic, Ordinary Families
| dc.creator | Pottharst, Jonathan | |
| dc.date | 2008-05-16 | |
| dc.date.accessioned | 2026-07-07T09:39:24Z | |
| dc.date.available | 2026-07-07T09:39:24Z | |
| dc.description | Let $p$ be an odd prime, and let $K/K_0$ be a quadratic extension of number fields. Denote by $K_\pm$ the maximal $\mathbb{Z}_p$-power extensions of $K$ that are Galois over $K_0$, with $K_+$ abelian over $K_0$ and $K_-$ dihedral over $K_0$. In this paper we show that for a Galois representation over $K_0$ satisfying certain hypotheses, if it has odd Selmer rank over $K$ then for one of $K_\pm$ its Selmer rank over $L$ is bounded below by $[L:K]$ for $L$ ranging over the finite subextensions of $K$ in $K_\pm$. Our method or proof generalizes a method of Mazur--Rubin, building upon results of Nekovář, and applies to abelian varieties of arbitrary dimension, (self-dual twists of) modular forms of even weight, and (twisted) Hida families. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/0805.2508 | |
| dc.identifier | http://arxiv.org/abs/0805.2508 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161159 | |
| dc.subject | Number Theory | |
| dc.subject | 11R23 (Primary), 11R34, 11R20 (Secondary) | |
| dc.title | Parity-induced Selmer Growth For Symplectic, Ordinary Families | |
| dc.type | text |